The 36-year-old joined the Premier League champions on a six-month loan from MLS franchise New York City FC after being released by Chelsea.
The midfielder is yet to make his debut for City due to fitness issues, but could get his chance either against Arsenal, Bayern Munich or his former club.
Summer signing Eliaquim Mangala is also in contention to play following his move from Porto for a reported £32m fee.
"Frank is ready," Pellegrini told reporters. "He has worked for about one month and he doesn't have any problems. Mangala is working normally and is in the squad list also.
"We have to play three games in a week so we will see if they play in these games. Both of them are ready to do it but I can't say which games they will play or if they will play."
City won their first two league games against Newcastle United and Liverpool, but lost 1-0 to Stoke City in their last outing before the international break.